PRICING AND VALUATION UNDER THE REAL-WORLD MEASURE

Gabriel Frahm ()
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Gabriel Frahm: Department of Mathematics/Statistics, Chair for Applied Stochastics and Risk Management, Helmut Schmidt University, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 01, 1-39

Abstract: In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I show that the aforementioned problems evaporate if the financial market is complete and sensitive. In this case, after an appropriate choice of the numéraire, the discounted price processes turn out to be uniformly integrable martingales under the real-world measure. This leads to a Law of One Price and a simple real-world valuation formula in a model-independent framework where the number of assets as well as the lifetime of the market can be finite or infinite.

Keywords: Arbitrage; complete market; complex market; efficient market; enlargement of filtrations; fundamental theorem of asset pricing; growth-optimal portfolio; immersion; numéraire portfolio; pricing; sensitive market; valuation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024916500060

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